Transcript Slides - Interactive Media & Game Development

Science of Fun
Ten Billion $/year from Six Thousand Slot Machines
Foxwoods Casino and Resort
What makes slots fun?
Pared-down Poker: Cutting to the Core of Command and Control.
Proc. of IEEE Symposium on Computational Intelligence and Games.
Analyzing humor (and fun) is like dissecting a frog.
Few people are interested and the frog dies of it....
E.B. White
Expected Utility ≡ Probability * Utility
“fair slots”
1*A = P*J
A = Anted
J = Jackpot
P = Prob.
The $20 Question
You have a choice between:
(s) a sure-thing of getting $20;
(g) a gamble with 20% chance of getting $100
and 80% chance of getting nothing.
The $80 Question
You have a choice between:
(s) a sure-thing of getting $80;
(g) a gamble with 80% chance of getting $100
and 20% chance of getting nothing.
De Martino et al. (2006). “Frames, Biases and Rational Decision
Making in the Human Brain”. Science, Vol. 313, pp 684-687.
average
Kahneman and Tversky (1979). “Prospect Theory: An Analysis of
Decision Under Risk”. Econometrica, Vol. 47, No. 2, pp 263-291.
Apparent Contribution from Aesthetic Utility = W - P
On a crusade in search of the Holy Grail… It’s Fun!
The Atoms of EVE’: A Bayesian Basis for Aesthetic Analysis…
Artificial Intelligence for Engineering Design, Analysis and Manufacturing (AIEDAM)
Expectation –
Violation
–
Explanation
Set-up
– Punchline –
Get-it?
Garden
–
Tragedy?
Analyzing humor
is like dissecting a frog.
Few people are interested…
Eaten
and the frog dies of it.
–
Comedy?
Per EVE’, Fun (S) is the sum of:
pleasure (p) from success in forming
Expectations (E)
+
pleasure (p’) from success in forming
Explanations (E’)
S = G*E + G’*E’
Expectation (E)
Win (P=Prob) Loss (Q=1-P)
E = P * log P + Q * log Q
Entropy of an event with Prob. P is defined as:
Unpredictability = Probability * Unexpectability
P
*
-log P
Entropy = (-P * log P) + (-Q * log Q)
Measure of Expectation (E)
This E is a negative entropy
Violation (V)
V = -E
Explanation (E’)
E’ = - [H+ * P * log P * R+ ] + [H- * Q * log Q * R-]
H+/H- = sense of humor
R = Bayesian resolution
Bayesian Belief (ρ is a Prob.)
posterior = prior * likelihood
R = ρ (Y|e) = ρ (Y) * ρ (e|Y)
e is evidence: win or loss
Y is hypothesis: “good luck” or “bad luck”
For slots, posterior = 1; R=+1 (win) or -1 (loss)
Measure of Explanation (E’)
H+/H- = 2
H+/H- = 1
Σ signed/weighted entropies
Fun = S = “S-thetic” utility
S = (G * E) + (G’ * E’)
G’/G = call to adventure
Fun = S = “S-thetic” utility
Goldilocks Function: S = G*E + G’*E’
Assumed by Prospect Theory
Derived by EVE’s Theory
Twenty-one Bell Three Wheel Nickel Slot Machine (Rake = 6%).
Has 8 different payoff combinations/probabilities, w/ Pagg = 13%.
Game of Skill (Punch Out)
EVE’ Model
WPI Data
Performance vs. Enjoyment
1
0.8
Mean Enjoyment
0.6
0.4
0.2
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
-0.2
-0.4
-0.6
-0.8
-1
Margin of Victory
Relating Cognitive Models of Computer Games to User Evaluations of Entertainment.
P. Piselli, Masters Thesis, WPI Department of Computer Science, 2006.
EVE’s Fun Functions
E = log P
V = -log P
E’ = -log P * H * R
EVE’s Fun Factors
H+/H- = sense of humor
G’/G = call to adventure
F
= price for pleasure
Shlomo Dubnov
“Thoughts About Memex”.
http://music.ucsd.edu/~sdubnov
Memex Music
Memex, the machine (Bush 1945), was a futuristic device,
For creating and recalling associations –
In the form of memory trails.
Memex, the music (Dubnov 2006), is an algorithmic composition,
Designed to create new music from old music –
By associations along probabilistic trails.
Let’s say that the current note in Memex is G - taken from Bach. To get the next note:
The machine will step forward with probability Q - or jump backward with probability P
Where jump backward is to the same note (different song) with “most similar” history.
Bach: … C D F E C G C…
Q
P
Beethoven: …A F E C G A C…
4
Mozart: … D C G B B A …
2
If it steps, the next note is C.
If it jumps, the next note is A.
Beethoven’s 4 > Mozart’s 2.
Fun (flow) function computed by EVE’ with same G’/G as for slots.
All E’ was assumed to be positive and Resolution (R) was set to Q2.
P was tweaked by the human creator until the machine composition
sounded “best”, which turned out to be much like slots – a P of 13%.
EVE’s Entropy: A Formal Gauge of Fun in Games. In:
Advanced Intelligent Paradigms in Computer Games.
SCIENCE OF FUN
Imagine a community with thousands of people sitting at machines playing games for
hours. What makes it fun? Is it virtual reality? Is it engaging narrative? Is it
multiplayer interaction? Actually, it’s none of the above. The community is Foxwoods
and the machines are slots. I’ll bet that slots are the most popular and profitable
machine game of all time – more than any modern computer game. I also think that
research and development in digital media has not done much to advance a scientific
understanding of fun in any game. So I cut to the chase, dissecting the aesthetic
experience using mathematical analyses and psychological experiments. I look at
gambling, music and artwork. I show how formal notions of Bayesian probability and
Shannon entropy can explain and predict feelings of pleasure. I have some demos to
make the math fun. I guarantee you have never seen fun like this before.
Historical
Ch 1: “Slots of Fun, Slots of Trouble:
An Archaeology of Arcade Gaming”
Cultural
“Rise of Aesthetics”
Sociological
Ch 24: “Games as the Play of Pleasure”
Psychological
“Optimal Experience”
Neurological
“Surprise!”
Personal
Pg 46: “Fun is just another word for learning”.
Informational
Shannon Theory
Perceptual
Bayesian Theory
Behavioral
Prospect Theory
Mathematical
Psychological-Neurological
Theoretical
Computing Comedy
Philosophical
Causality and Probability
www.tracsgame.com
On TRACS: Dealing with a Deck of Double-sided Cards
Proc. IEEE Symposium on Comp. Intelligence and Games.